document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750473>Question 750473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you so much. These are homework problems, and I am a straight-A student. I am not trying to be cheap, I just seriously don't understand it. I have tutoring tomorrow, and need to know how to do these by then. Thanks for your help. It is greatly appreciated! :)\r<BR>\n" );
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document.write( "1. The junior prom committee brought in $6300 through ticket sales last year. This year they<BR>\n" );
document.write( "had hoped to increase attendance by lowering the ticket price by $3. They ended up selling 48 more tickets for a total of $5970.<BR>\n" );
document.write( "a. What was the original price per ticket?<BR>\n" );
document.write( "b. How many tickets were sold at the lower price?\r<BR>\n" );
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document.write( "2. When Raj shined his flashlight on the wall at an angle, it made an ellipse with a vertical major axis of 34 inches and a horizontal minor axis of 18 inches. Let the center of the ellipse be the origin of a coordinate system. Find an equation for the edge of the ellipse. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456597 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. The junior prom committee brought in $6300 through ticket sales last year. This year they<BR>\n" );
document.write( "had hoped to increase attendance by lowering the ticket price by $3. They ended up selling 48 more tickets for a total of $5970.<BR>\n" );
document.write( "a. What was the original price per ticket?<BR>\n" );
document.write( "h = # of tix at higher price<BR>\n" );
document.write( "p = higher price<BR>\n" );
document.write( "h*p = 6300<BR>\n" );
document.write( "(h+48)*(p-3) = 5970<BR>\n" );
document.write( "h = 6300/p<BR>\n" );
document.write( "(6300/p + 48)*(p-3) = 5970<BR>\n" );
document.write( "(6300 + 48p)*(p-3) = 5970p<BR>\n" );
document.write( "(2100 + 16p)*(p-3) = 1990p<BR>\n" );
document.write( "16p^2 + 2052p - 6300 = 1990p<BR>\n" );
document.write( "8p^2 + 31p - 3150 = 0<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2%2B31x%2B-3150+=+0 ALIGN=MIDDLE  ALT=\"8x%5E2%2B31x%2B-3150+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2831%29%5E2-4%2A8%2A-3150=101761 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2831%29%5E2-4%2A8%2A-3150=101761\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=101761 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-31%2B-sqrt%28+101761+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-31%2B-sqrt%28+101761+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2831%29%2Bsqrt%28+101761+%29%29%2F2%5C8+=+18 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2831%29%2Bsqrt%28+101761+%29%29%2F2%5C8+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2831%29-sqrt%28+101761+%29%29%2F2%5C8+=+-21.875 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2831%29-sqrt%28+101761+%29%29%2F2%5C8+=+-21.875\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2%2B31x%2B-3150 ALIGN=MIDDLE  ALT=\"8x%5E2%2B31x%2B-3150\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8x%5E2%2B31x%2B-3150+=+%28x-18%29%2A%28x--21.875%29 ALIGN=MIDDLE  ALT=\"8x%5E2%2B31x%2B-3150+=+%28x-18%29%2A%28x--21.875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 18, -21.875.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B31%2Ax%2B-3150+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B31%2Ax%2B-3150+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "==========================<BR>\n" );
document.write( "p = $18 (original price)<BR>\n" );
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document.write( "b. How many tickets were sold at the lower price?<BR>\n" );
document.write( "Tix at $18 = 6300/18 = 350<BR>\n" );
document.write( "350 + 48 = 398 at the lower price<BR>\n" );
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document.write( "2. When Raj shined his flashlight on the wall at an angle, it made an ellipse with a vertical major axis of 34 inches and a horizontal minor axis of 18 inches. Let the center of the ellipse be the origin of a coordinate system. Find an equation for the edge of the ellipse.<BR>\n" );
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document.write( "18/2 = 9<BR>\n" );
document.write( "34/2 = 17<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F9%5E2+%2B+y%5E2%2F17%5E2+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F9%5E2+%2B+y%5E2%2F17%5E2+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F81+%2B+y%5E2%2F289+=+1 ALIGN=MIDDLE  ALT=\"x%5E2%2F81+%2B+y%5E2%2F289+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );